Book cover for Thermodynamics: An Engineering Approach

Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

ISBN #9781259822674

9th Edition

2,694 Questions

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59,300 Students Helped

Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

The chapter on Refrigeration Cycles provides a comprehensive framework for the analysis and design of various refrigeration systems. It emphasizes the importance of directly measurable properties and their interrelations through partial derivatives and Maxwell relations. Key thermodynamic tools such as the Clapeyron equation, specific heats, and the Jouleā€“Thomson coefficient are introduced, enabling engineers to evaluate and optimize systems such as vapor-compression, absorption, and gas refrigeration cycles. A strong understanding of these principles is essential for effective second-law analysis and the proper selection of refrigerants in both industrial and specialized applications.

Learning Objectives

1

Analyze the fundamental thermodynamic principles underlying refrigeration cycles, including measurable and indirectly determined properties.

2

Explain the role of partial derivatives, Maxwell relations, and the Clapeyron equation in evaluating latent heats and property changes.

3

Evaluate various refrigeration cycles such as the reversed Carnot cycle, vapor-compression cycles (ideal and actual), and absorption systems.

4

Apply second-law analysis and assess the selection criteria for refrigerants in practical thermodynamic systems.

5

Demonstrate the use of concepts like specific heats and the Jouleā€“Thomson coefficient in the design and optimization of refrigeration systems.

Key Concepts

CONCEPT

DEFINITION

Thermodynamic Properties

Directly measurable properties such as pressure (P), volume (v), and temperature (T), along with indirectly measured ones like internal energy, enthalpy, and entropy.

Maxwell Relations

A set of equations derived from the second law of thermodynamics that relate different partial derivatives of thermodynamic properties.

Clapeyron Equation

An equation that relates the pressure, specific volume, and temperature during a phase change, used to compute latent heats.

Specific Heats (cv and cp)

Quantities that measure the energy required to raise the temperature of a substance at constant volume (cv) or pressure (cp).

Jouleā€“Thomson Coefficient

A parameter that quantifies the temperature change of a gas when it is forced through a valve or porous plug (throttling process) without external work.

Example Problems

Example 1

Why do we study the reversed Carnot cycle even though it is not a realistic model for refrigeration cycles?

Example 2

Why is the reversed Carnot cycle executed within the saturation dome not a realistic model for refrigeration cycles?

Example 3

A steady-flow Carnot refrigeration cycle uses refrigerant- $134 \mathrm{a}$ as the working fluid. The refrigerant changes from saturated vapor to saturated liquid at $60^{\circ} \mathrm{C}$ in the condenser as it rejects heat. The evaporator pressure is $180 \mathrm{kPa}$. Show the cycle on a $T-s$ diagram relative to saturation lines, and determine $(a)$ the coefficient of performance, (b) the amount of heat absorbed from the refrigerated space, and (c) the net work input.

Example 4

Refrigerant-134a enters the condenser of a steady-flow Carnot refrigerator as a saturated vapor at 90 psia, and it leaves with a quality of $0.05 .$ The heat absorption from the refrigerated space takes place at a pressure of 30 psia. Show the cycle on a $T-s$ diagram relative to saturation lines, and determine $(a)$ the coefficient of performance, $(b)$ the quality at the beginning of the heat-absorption process, and $(c)$ the net work input.

Example 5

Does the ideal vapor-compression refrigeration cycle involve any internal irreversibilities?
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Step-by-Step Explanations

QUESTION

How can the latent heat of a phase change be calculated given pressure, specific volume, and temperature data?

STEP-BY-STEP ANSWER:

Step 1: Write down the Clapeyron equation: dP/dT = L/(T(v_g - v_f)), where L is the latent heat and v_g, v_f are the specific volumes of the gas and liquid phases respectively.
Step 2: Obtain or measure the values of pressure, specific volumes, and temperature for the phase change process.
Step 3: Compute the derivative dP/dT from the available data or provide an approximation if the data varies linearly.
Step 4: Rearrange the equation to solve for the latent heat L: L = T(v_g - v_f) * (dP/dT).
Step 5: Substitute the numerical values into the equation and calculate L.
Final Answer: The latent heat is calculated as L = T*(v_g - v_f)*(dP/dT).

Clapeyron Equation Application

QUESTION

How can the coefficient of performance (COP) for a reversed Carnot cycle be determined based on the temperature limits?

STEP-BY-STEP ANSWER:

Step 1: Recognize that in a reversed Carnot refrigeration cycle, the COP is defined as COP = T_low / (T_high - T_low), where T_low is the refrigerating temperature and T_high is the ambient temperature.
Step 2: Ensure that the temperatures are in an absolute scale (Kelvin).
Step 3: Substitute the known temperature values for T_low and T_high into the expression.
Step 4: Perform the arithmetic operations to find the COP value.
Final Answer: The coefficient of performance for the reversed Carnot cycle is COP = T_low/(T_high - T_low).

Reversed Carnot Cycle Efficiency

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Common Mistakes

  • Assuming that all refrigeration cycles operate under ideal conditions without considering real gas behavior.
  • Misinterpreting the direction of energy flow in reversed cycles versus conventional cycles.
  • Overlooking the importance of using absolute temperature scales for energy calculations.
  • Neglecting the effects of departure functions when evaluating real-gas properties.
  • Confusing the roles and applications of Maxwell relations with other thermodynamic identities.